Finite Group Databasebeta

← #17995761

Subgroups — #17995761

Order 4736.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558159C211yesmaximal, characteristic, complemented
2#14557388C211yesmaximal, characteristic
3#14557388C212yesmaximal
4#14557299C212yesmaximal, complemented
5C37×#342C211yesmaximal, characteristic, complemented
6C24×D37C2211yescharacteristic
7#11924515—22no—
8#11924513—24no—
9C2×C22⋊Dic37C2211yescharacteristic
10C2×C22⋊Dic37C2212yes—
11C2×#10596938—22no—
12C2×#10596938—24no—
13C2×C22⋊C4×C37C2212yes—
14C2×C22⋊C4×C37C2211yescharacteristic
15C24×C37C2311yescharacteristic
16C23×D37—21no—
17C23×D37—22no—
18C23×D37—22no—
19C23×D37—21no—
20C23×D37—44no—
21C23×D37Q812yescomplemented
22C22×C4×C37—22no—
23C22×C4×C37D412yes—
24C22×Dic37—21no—
25C22×Dic37D414yes—
26C2×Dic74—22no—
27C22⋊C4×C37—22no—
28C22⋊C4×C37—22no—
29C22⋊C4×C37—22no—
30C22⋊Dic37—22no—
31C22⋊Dic37—22no—
32C22⋊Dic37—22no—
33#10596938—48no—
34#10596938—44no—
35C4⋊Dic37—22no—
36#10596936—24no—
37C23×C37—42no—
38C23×C37C2×D411yescharacteristic
39C23×C37C2×D412yes—
40C23×C37C2×Q811yescharacteristic
41C23×C37#4112yes—
42C23×C37#4111yescharacteristic
43C22×D37—24no—
44C22×D37—28no—
45C22×D37—24no—
46C22×D37—22no—
47C22×D37—44no—
48C22×D37—48no—
49C22×D37—44no—
50C22×D37—42no—
51C22×D37—44no—
52C22×D37—41no—
53C22×D37—42no—
54C22×D37—41no—
55C2×C4×C37—22no—
56C2×C4×C37—42no—
57C2×C4×C37—44no—
58C2×C4×C37—42no—
59C2×Dic37—24no—
60C2×Dic37—44no—
61C2×Dic37—42no—
62C2×Dic37—41no—
63Dic74—82no—
64C22×C37—22no—
65C22×C37—24no—
66C22×C37—41no—
67C22×C37—42no—
68C22×C37—41no—
69C22×C37#12011yescharacteristic
70C22×C37C22⋊Q812yes—
71C22×C37C22⋊Q811yescharacteristic
72C22×C37#12412yes—
73C22×C37#12411yescharacteristic
74C2×D37—28no—
75C2×D37—24no—
76C2×D37—44no—
77C2×D37—48no—
78C2×D37—44no—
79C2×D37—42no—
80C2×D37—42no—
81C2×D37—44no—
82C4×C37—42no—
83C4×C37—82no—
84Dic37—44no—
85Dic37—81no—
86#2029—371nomaximal, Sylow
87C2×C37—21no—
88C2×C37—22no—
89C2×C37—22no—
90C2×C37—21no—
91C2×C37#39311yescharacteristic
92C2×C37B(4,𝔽2)12yes—
93D37—44no—
94#543—371no—
95#379—372no—
96#379—371no—
97#342—372no—
98#342D3711yescharacteristic, complemented
99C37#202911yescharacteristic, complemented, Sylow
100C25—371no—
101C22⋊Q8—744no—
102C22⋊Q8—742no—
103C2×C22⋊C4—372no—
104C2×C22⋊C4—371no—
105C2×C22⋊C4—744no—
106C2×C22⋊C4—742no—
107C2×C22⋊C4C2×D3712yes—
108C2×C22⋊C4C2×D3711yescharacteristic
109C24—372no—
110C24—741no—
111C24—742no—
112C24—742no—
113C24—741no—
114C24—1484no—
115C24C22×D3711yescharacteristic
116C2×Q8—742no—
117C22×C4—22no—
118C22×C4—374no—
119C22×C4—741no—
120C22×C4D14812yes—
121C4⋊C4—744no—
122C4⋊C4—742no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—742no—
127C22⋊C4—742no—
128C22⋊C4—742no—
129C22⋊C4—1484no—
130C22⋊C4—1488no—
131C23—42no—
132C23—744no—
133C23—748no—
134C23—744no—
135C23—742no—
136C23—1482no—
137C23—1484no—
138C23—1484no—
139C23—1488no—
140C23—1484no—
141C23—1481no—
142C23—1482no—
143C23—1481no—
144C23C2×D14811yescharacteristic
145C23#1059696212yes—
146C23D4×D3712yes—
147C23#1059696411yescharacteristic
148C23Q8×D3711yescharacteristic
149Q8—2962no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—744no—
155C2×C4—1482no—
156C2×C4—1481no—
157C2×C4—1484no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—748no—
164C22—744no—
165C22—1488no—
166C22—1484no—
167C22—1484no—
168C22—1482no—
169C22—1482no—
170C22—1484no—
171C22#1192450611yescharacteristic
172C22#1192451412yes—
173C22#1192451611yescharacteristic
174C22#1192452212yes—
175C22#1192452411yescharacteristic
176C4—42no—
177C4—82no—
178C4—2961no—
179C4—1484no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—1484no—
185C2#1455744611yescharacteristic
186C2#1455772112yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC24×C37C23
FrattiniC24C22×D37
FittingC37×#342C2
socleC22×C37#120
prime radicalC24×D37C22
hypercenter#342D37
hypocenterC37#2029
LCSG ▷ C24×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14558159C2semidirect
4. #14557299C2semidirect
5. C37×#342C2semidirect
21. C23×D37Q8semidirect
98. #342D37semidirect
99. C37#2029semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145581592
#145573882
#145572992
C37×#3422
#202937